Using an electric mixer or stand mixer, cream together the butter and sugars until light and creamy. Add in the peanut butter, egg, and vanilla. Mix until combined. Be sure to scrape down the sides of the bowl and mix again.
In a separate large bowl, combine the flour, salt, baking soda, and baking powder. Add wet ingredients and mix just until combined and a dough has formed.
Cover the bowl with plastic wrap and place it in the refrigerator for at least two hours before baking.
Preheat oven to 350 degrees F and line two cookie sheets with parchment paper. Roll cookies into 22 balls by using a mini ice cream scoop. Place 11 cookies on each prepared cookie sheets. Flatten with your hand just a tiny bit and bake in the center rack (one cookie sheet at a time) for 10 minutes.
Remove cookies from oven, and let rest for two minutes. Push Reese's cups in the center of each cookie, pressing gently. Let them sit for another five minutes before removing them to the cooling rack. Enjoy!